Question

Find the missing part for A, Y, Z, and B.

Answer 1

All (3) of the triangles are similar to one another, and they have the 30-60-90 interior-angle pattern. This allows us to establish the following relations.

$a+b=2x\implies x=\dfrac{15}2$


$z=\sqrt3\,x\implies z=\dfrac{15\sqrt3}2$


$\dfrac ax=\dfrac x{a+b}\implies a(a+b)=x^2\implies15a=\dfrac{15^2}{2^2}\implies a=\dfrac{15}4$


$a+b=15\implies b=15-\dfrac{15}4=\dfrac{45}4$


$y=\sqrt3\,a\implies y=\dfrac{15\sqrt3}4$